Hidden Variables and the Two Theorems of John Bell

Hidden Variables and the Two Theorems of John Bell

1993 | N. David Mermin
N. David Mermin's article, "Hidden Variables and the Two Theorems of John Bell," published in *Reviews of Modern Physics* in 1993, revisits and critiques the no-hidden-variables theorems, particularly focusing on the Kochen-Specker (KS) theorem and Bell's Theorem. Mermin highlights the simplicity and clarity of recent versions of the KS theorem, which can be easily understood by physicists and philosophers alike. He also discusses the historical context, including von Neumann's flawed proof of the non-existence of hidden variables and Bell's criticism of it. Mermin provides detailed proofs of the KS theorem in 3, 4, and 8-dimensional state spaces, demonstrating that it is impossible to assign pre-existing values to observables in a way that is consistent with quantum mechanics. He emphasizes the importance of non-contextuality, the idea that the value of an observable should not depend on the context in which it is measured, and how this assumption can be replaced by locality in Bell's Theorem. The article concludes by exploring the implications of these theorems for the understanding of quantum mechanics and the nature of reality, suggesting that the results are not merely philosophical but have profound implications for the foundations of physics.N. David Mermin's article, "Hidden Variables and the Two Theorems of John Bell," published in *Reviews of Modern Physics* in 1993, revisits and critiques the no-hidden-variables theorems, particularly focusing on the Kochen-Specker (KS) theorem and Bell's Theorem. Mermin highlights the simplicity and clarity of recent versions of the KS theorem, which can be easily understood by physicists and philosophers alike. He also discusses the historical context, including von Neumann's flawed proof of the non-existence of hidden variables and Bell's criticism of it. Mermin provides detailed proofs of the KS theorem in 3, 4, and 8-dimensional state spaces, demonstrating that it is impossible to assign pre-existing values to observables in a way that is consistent with quantum mechanics. He emphasizes the importance of non-contextuality, the idea that the value of an observable should not depend on the context in which it is measured, and how this assumption can be replaced by locality in Bell's Theorem. The article concludes by exploring the implications of these theorems for the understanding of quantum mechanics and the nature of reality, suggesting that the results are not merely philosophical but have profound implications for the foundations of physics.
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